Big Idea:
Students look at a variety of models for solving and modeling equations with rational coefficients.

I include Warm ups with a Rubric as part of my daily routine. My goal is to allow students to work on Math Practice 3 each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. The Video Narrative explains this lesson’s warm up which asks students to determine whether an equation with rational numbers is actually equivalent.

I also use this time to correct and record the previous day's Homework.

Resources

We begin with: Suppose one painter can paint the entire house in twelve hours, and the second painter takes eight hours. How long would it take the two painters together to paint the house? (Math Practice 4) I use the Note Card Activity with this problem. There are so many great correct and incorrect answers that can come from this problem. Some scaffolding may be necessary as this problem may seem difficult to some (Math Practice 1). For example, I may ask students what portion of the house each painter can finish in one hour.

We then do an additional problem to allow those students that really struggled with the first one to try some of the methods they saw (Math Practice 5).

Resources

The remainder of the lesson is Guided Practice. For these, I walk around and ask students with a range of different solution methods to share their work on the board as well as explain their steps (Math Practice 3). If no one was able to finish it, we find the solution by graphing as a class.